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SP 2005 CH 3 DT Systems 2

SP 2005 CH 3 DT Systems 2 - EE 3120 Chapter 3 Time Domain...

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Unformatted text preview: EE 3120 Chapter 3 Time Domain Analysis of Discrete-Time Systems R R R R R R R R R E … … 2 V 1 V V n V 1 n V- 1 m V- 1 n V + Resistive Ladder Circuit, we can derive a difference to express voltage as a function of node position . From the circuit: , m V E V = = 1 2 3 1 1 1 1 1 1 KCL at node : 3 0, for 1,2,... 1 n n n n n n n n n n n n n n i i i V V V V V R R R V V V V V V V V n m- +- +- + = +-- = +- = +-- + = =- 1 i 2 i 3 i For example: If m=4. find all node voltages: 1 2 2 1 1 2 3 3 2 1 1 1 3 1 1: 3 3 2: 3 3 3(3 ) 8 3 V E n V V V V V E n V V V V V V V E V V V E = =- + = =- =- + = =- =-- =- R R R R R R R R R E … … 2 V 1 V V n V 1 n V- 1 m V- 1 n V + 1 i 2 i 3 i 2 3 4 4 3 2 1 1 4 1 3: 3 3 3(8 3 ) 3 21 8 n V V V V V V V E V E V V E = - + = = - = - - - = - 4 1 8 0, 21 V V E = = 2 2 8 8 3 21 7 7 E V E E E E V = - = - = = 3 3 8 8 3 21 21 E V E E V = - = = Variation of the Bank Account Debt reduction or Loan Amortization: [ ] is the debt owed on a loan in month . y n n [0] is the initial loan amount y Loan must be reduced to 0 after years, y[N 12], for a total of N 12 EQUAL payments, [ ] N x n p = Annual interest rate . Interest /12 applied to balance each month. r r [ ] [ 1] [ 1] [ ] [ 1](1 ) y n y n ry n x n y n r p =- +-- =- +- [1] [0](1 ) y y r p = +- 2 3 2 [2] [1](1 ) [0](1 ) (1 ) [3] [2](1 ) [0](1 ) [(1 ) (1 ) 1] y y r p y r p r p y y r p y r p r r = +- = +- +- = +- = +- +...
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SP 2005 CH 3 DT Systems 2 - EE 3120 Chapter 3 Time Domain...

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